Here's my work for finding [p]subscript B:
I have the equation p(x)=3-8x+2x^2-6x^3 and B=(1+x+x^2+x^3, 1+x+x^2, 1+x, 1).
I said a(1+x+x^2+x^3)+b(1+x+x^2)+c(1+x)+d=3-8x+2x^2-6x^3.
I solved for a,b,c,d and got:
a=-6
b+a=2
a+b+c=-8
a+b+c+d=3

Thus, a=-6, b=8, c=-10, d=11.

So I said that [p]subscriptB is the vector:
[-6
8
-10
11]
, but this is obviously not right.

Here's my work for finding [p]subscript B:
I have the equation p(x)=3-8x+2x^2-6x^3 and B=(1+x+x^2+x^3, 1+x+x^2, 1+x, 1).
I said a(1+x+x^2+x^3)+b(1+x+x^2)+c(1+x)+d=3-8x+2x^2-6x^3.
I solved for a,b,c,d and got:
a=-6
b+a=2
a+b+c=-8
a+b+c+d=3

Thus, a=-6, b=8, c=-10, d=11.

So I said that [p]subscriptB is the vector:
[-6
8
-10
11]
, but this is obviously not right.